Problem: $\dfrac{ -4g - 8h }{ -2 } = \dfrac{ g - 6i }{ -6 }$ Solve for $g$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ -4g - 8h }{ -{2} } = \dfrac{ g - 6i }{ -6 }$ $-{2} \cdot \dfrac{ -4g - 8h }{ -{2} } = -{2} \cdot \dfrac{ g - 6i }{ -6 }$ $-4g - 8h = -{2} \cdot \dfrac { g - 6i }{ -6 }$ Multiply both sides by the right denominator. $-4g - 8h = -2 \cdot \dfrac{ g - 6i }{ -{6} }$ $-{6} \cdot \left( -4g - 8h \right) = -{6} \cdot -2 \cdot \dfrac{ g - 6i }{ -{6} }$ $-{6} \cdot \left( -4g - 8h \right) = -2 \cdot \left( g - 6i \right)$ Distribute both sides $-{6} \cdot \left( -4g - 8h \right) = -{2} \cdot \left( g - 6i \right)$ ${24}g + {48}h = -{2}g + {12}i$ Combine $g$ terms on the left. ${24g} + 48h = -{2g} + 12i$ ${26g} + 48h = 12i$ Move the $h$ term to the right. $26g + {48h} = 12i$ $26g = 12i - {48h}$ Isolate $g$ by dividing both sides by its coefficient. ${26}g = 12i - 48h$ $g = \dfrac{ 12i - 48h }{ {26} }$ All of these terms are divisible by $2$ $g = \dfrac{ {6}i - {24}h }{ {13} }$